Identification Problems in GMM Estimation of the Covariance Structure of Earnings

Donal O'Neill, Olive Sweetman, Aedin DorisNUI Maynooth, Ireland

The last decade has seen rapid growth in the number of empirical studies that distinguish between two components of aggregate inequality: inequality that reflects differences across individuals due to permanent characteristics and inequality arising from transitory shocks. Most of these studies have combined panel data with the Generalised Method of Moments estimator to estimate the parameters of interest. Moffitt and Gottschalk (2008) draw attention to the fact that identification of the parameters of this model requires a long panel. However, there has been no study that provides a detailed analysis of identification of the GMM estimator under the conditions typically encountered in earnings panel data. In this paper, we fill this gap by examining the sensitivity of parameter identification to key features such as panel length, number of observations and the degree of persistence of earnings shocks. We show that, when earnings shocks have high persistence, a panel such as the European Community Household Panel with only eight years of observations will not yield satisfactory results. We experiment with panels of different lengths to determine the minimum panel length needed. Using both analytical and Monte Carlo techniques, we also draw attention to another identification problem that occurs, this time when earnings shocks have low persistence. We show that the standard asymptotic results for a number of the structural parameters are not applicable in this case. However, even with short panels, we show that the estimator provides reasonable predictions of the key, policy-relevant features of the model.